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Proof step 83 from proof inv-replay (previous step)

fs0[ri[key]] = datanode(key0, buf), key0 = key, replay-log(log0, fs0, fi0 ⊖ fo0) = ri ⊖ ro, fs0[ri[key]].data?, ro.inodes?, fo0.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-closed(ri, fs0, ro), ri-inj(fi0), ri-inj(ri), ri[key] ∈ fs0, inodekey(key.ino) ∈ ro, key ∈ ri, inodekey(key.ino) ∈ ri, fo0 ⊆ dom fi0, ro ⊆ dom ri, key.inode? → fs0[ri[key]].inode? ∧ key.ino ≠ 0, key.dentry? → fs0[ri[key]].dentry? ⊦ # ro = 0, ro = ∅, key.data?, dups(log0), inodekey(0) ∈ ri ⊖ ro, inodekey(0) ∈ ri, key ∈ ro, (¬ fs0[ri[key]].dentry? ∧ ¬ fs0[ri[inodekey(key.ino)]].directory ∧ # buf = VFS_PAGE_SIZE → key ∈ ri ⊖ ro → ¬ fs0[ri[key]].data?) ∧ file-node-cons(fs0, ri ⊖ ro) ∧ orphans-cons(fs0, ri ⊖ ro, ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
fs0[ri[key]] = datanode(key, buf), replay-log(log0, fs0, fi0 ⊖ fo0) = ri ⊖ ro, ro.inodes?, fo0.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-closed(ri, fs0, ro), ri-inj(fi0), ri-inj(ri), ri[key] ∈ fs0, inodekey(key.ino) ∈ ro, key ∈ ri, inodekey(key.ino) ∈ ri, fo0 ⊆ dom fi0, ro ⊆ dom ri ⊦ # ro = 0, ro = ∅, key.data?, key.dentry?, key.inode?, dups(log0), inodekey(0) ∈ ri ⊖ ro, inodekey(0) ∈ ri, key ∈ ro, (¬ fs0[ri[inodekey(key.ino)]].directory ∧ # buf = VFS_PAGE_SIZE → ¬ key ∈ ri ⊖ ro) ∧ file-node-cons(fs0, ri ⊖ ro) ∧ orphans-cons(fs0, ri ⊖ ro, ∅)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ datanode(key, buf).dentry?; (s)% ⊦ ¬ datanode(key, buf).inode?; (s)% ⊦ datanode(key, buf).data?; (s)